Obviously something that compaq placed in the software bundle. as such have you run it and seen what happens?
From the sound of it it may be internet security for the system, or a log keeper of visited sites, something along those lines.
Unfortunately a search of Compaq's site hasn't turned up anything, but you have not listed the system, etc. So I have nothing more than a basic search available to me for this.
You likely can remove it without issue, you may wish to open regedit and search for watchdog.exe, as if it runs in the backround, you could find it in there where it is instructed to run or run once, and you could just remove that key as well.